Tiling a deleted 64 grid using dominos

This is a classic problem that can be found in most books on problem solving and I re-encountered on my reading of Mathematics a Very Short Introduction by Timothy Gower. The problem is if you delete the two diagonal squares of a 64 grid squares like a chess board and then you have to tile it using dominos. The way to do is to think of is to realize that each domino occupies a black and white square. Assuming that the two black squares were deleted. There are now 62 squares in total out of which 32 are white and 30 are black. So no matter how we tile. We will be left with 2 white squares and since a domino tiles only black and white those two will remain untiled.